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arXiv · 1512.06765

Modular Form Representation for Periods of Hyperelliptic Integrals

Keno Eilers
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Abstract

To every hyperelliptic curve one can assign the periods of the integrals over the holomorphic and the meromorphic differentials. By comparing two representations of the so-called projective connection it is possible to reexpress the latter periods by the first. This leads to expressions including only the curve's parameters $λ_j$ and modular forms. By a change of basis of the meromorphic differentials one can further simplify this expression. We discuss the advantages of these explicitly given bases, which we call Baker and Klein basis, respectively.

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Keno Eilers. 2016-06-24. Modular Form Representation for Periods of Hyperelliptic Integrals. https://doi.org/10.3842/sigma.2016.060

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